252 H. K. SCHACHMAN AND 11. C. WILLIAMS 



Mandelkern (1953), who also made the point that these calculations give a 

 value of the axial ratio of an ellipsoid of revolution that is equivalent to, 

 but not necessarily identical with, the real particle. Distortion of the macro- 

 molecule or any motion of liquid through the particle during its migration 

 through the liquid would vitiate the correspondence between the calculated 

 particle and the real one since the hydrodynamic theories assume rigid 

 objects (any water of hydration must be immobilized and move with the 

 particle as a unit). Other types of investigations into the physical-chemical 

 properties of proteins and viruses have led to the widely adopted view that 

 these materials are only slightly hydrated and that the swollen particles do 

 act as rigid particles, as required by the hydrodynamic theories. For such 

 materials, Equation 18 is applicable, and knowledge of the hydration (w) 

 permits the calculation of the axial ratio directly from the diffusion coeffi- 

 cient. It is interesting to note that ^ is not sensitive to axial ratio for par- 

 ticles that are almost spherical. Therefore, Equation 19 can be used for 

 molecular weight calculations if the electron microscope reveals that the 

 particles are not elongated. 



5. Ultracentrifugation 



a. Introduction. Ultracentrifuges can be used in either of two ways which 

 differ both experimentally and theoretically. In one, the centrifugal field is 

 so large that the force on the solute molecules causes them to migrate 

 through the solution rapidly, and the velocity of movement of the molecules 

 is measured during the sedimentation. In the other, the centrifugal field is so 

 small that the rate of motion of the particles is not the quantity that is 

 measured. Instead, an equilibrium state is established after a long period 

 of centrifugation and the concentration of the solute, although varying 

 slightly at each level in the cell and being finite everywhere, no longer varies 

 with time. Interpretation of the results of this type of experiment is based 

 on measurements of the concentration of the solute as a function of position 

 within the centrifuge cell. For the theoretical and experimental development 

 of each of these ultracentrifugal methods, we owe much to the pioneer work 

 of Svedberg and his collaborators (Svedberg and Pedersen, 1940). 



The former method is known as the sedimentation velocity method and 

 has, to date, been the one more widely used. In a sedimentation velocity 

 experiment, the ultracentrifuge rotor is operated at speeds up to 60,000 

 r.p.m., corresponding to forces of 250,000 times that of gravity. Molecules 

 which initially were uniformly distributed throughout the solution in the 

 ultracentrifuge cell are caused to settle at appreciable rates toward its 

 periphery. This migration of the solute molecules creates, in effect, three 

 regions within the ultracentrifuge ceU. One of these is the zone containing 

 only solvent molecules and is termed the supernatant. Another is the region 



